---
res:
  bibo_abstract:
  - "We prove near-optimal upper bounds for the oddmoments of the distribution of
    coprime residues inshort intervals, confirming a conjecture of Montgomeryand Vaughan.
    As an application, we prove near-optimalupper bounds for the average of the refined
    singularseries in the Hardy–Littlewood conjectures concerningthe number of prime
    \U0001D458-tuples for \U0001D458 odd. The mainnew ingredient is a near-optimal
    upper bound for thenumber of solutions to ∑1 ⩽\U0001D456 ⩽\U0001D458\U0001D44E
    \U0001D456\U0001D45E\U0001D456∈ ℤ when \U0001D458 is odd,with gcd(\U0001D44E\U0001D456
    , \U0001D45E\U0001D456 ) = 1 and restrictions on the size of thenumerators and
    denominators, which is of indepen-dent interest.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Thomas F.
      foaf_name: Bloom, Thomas F.
      foaf_surname: Bloom
  - foaf_Person:
      foaf_givenName: Vivian Zieve
      foaf_name: Kuperberg, Vivian Zieve
      foaf_surname: Kuperberg
      foaf_workInfoHomepage: http://www.librecat.org/personId=c3bac823-112d-11f0-a3f5-c264f852e697
  bibo_doi: 10.1112/plms.70068
  bibo_issue: '1'
  bibo_volume: 131
  dct_date: 2025^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0024-6115
  - http://id.crossref.org/issn/1460-244X
  dct_language: eng
  dct_publisher: Wiley@
  dct_title: Odd moments and adding fractions@
...